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5>C
THEORY OF THE TRANSFORMER FOR THE NEUTRALIZING
OF POWER INDUCTION IN TELEGRAPH CIRCUITS
BY
WILLIAM RIGA LYON
B. S. Worcester Polytechnic Institute, 1917
THESIS
Submitted in Partial Fulfillment of the Requirements for the
Degree of
MASTER OF SCIENCE
IN ELECTRICAL ENGINEERING
IN
THE GRADUATE SCHOOL
OF THE
UNIVERSITY OF ILLINOIS
1920
UNIVERSITY OF ILLINOISTHE GRADUATE SCHOOL
_ Jan. 16, ig2Q
I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPER-
VISION by .William... Pdga....I#<m.
ENTITLED H}he.Qz.y.....a£...the. Transx.o.r.me.r....xar. tlie Lle.u:fcrali.zlng..
of Power In&Tiotion in Tele.gra.ph....Girc.nit.s
BE ACCEPTED AS FULFILLING THIS PART OF THE REQUIREMENTS FOR THE
degree OF....Masiie.r of S.ci.e.n.c.e in....JS.le.ctxl.Q.al.....^g.ine.Qrin£.
Head of Department
Recommendation concurred in :*
Committee
on
Final Examination*
11Required for doctor's degree but not for master's.
It rt
/
Table of Contents
ListT-i +jjISX-
pageof Figuresof Curves
I INTRODUCTION
1. Power Line Induction 1
2. The neutralizing Transformer Defined 2
3. Its Applications 3
4. Acknowledgements 4
5. Statement of the General Problem 5
II GENERAL THEORY
1. Operation at Critical Frequency(a) Compensation of Power Line Induction 7
(b) Mutual Interference between TelegraphCircuits 11
2. Operation at Hon Critical Frequency-fa) Approximate Compensation of Power
Lin< Induction 15(b) Mutual Interference betvveen Telegraph
Circuits 17
III SPECIAL TYPES
1. Parallel Compensators Operating atCritical Frequency(a) Compensation of Power Line Indue tionl9(b) Mutual Interference between Telegraph
Circuits 21
2. Compensation by Audion Bulbs(a) Theory Applied to Correction of
Interference 24(b) Results 27
IV CONCLUSIONS
1. General Observations 28
2. Some Applications of the Theorv 29
List of Figures
figure page
1. Section view of a power line and a communication line 1
2. Longitudinal view of a power line and a communication linewith transposition 2
3. Section view of a power line and a communication line ofsingle conductor - ground return type 2
4. Sketch showing telegraph lines "being exposed to a parallelpowe r c i cqvS t 3
5. Compensating device applied to telegraph Circuits 46. Theoretical compensation at critical frequency 5
7. Approximate compensation at non critical frequency 5
8. Diagramatic view showing mutual interference between secondarycoils of the compensator 6
9. Vector diagram on the theory of compensation 8fa.0. Equivalent circuit diagram of neutralizing transformer 9
11 • Circuit diagram of transformer primary and parallel condenserlO12. Vector diagram of resistance, inductance and capacity 1013. Diagram of equivalent secondary impedance of system 1214. Circuit of the approximate equivalent secondary impedance 1315. Sketch of parallel compensators 2016. Vector diagram for compensation with parallel arrangement 2017. Equivalent secondary impedance with parallel compensators 2118. Effective resistance of circuits containing critical amount
of inductance and capacity 2219. Reduced circuit of equivalent secondary impedance 2220. Circuit showing compensation "by audions 2421. Plate current - grid voltage characteristic of audion 2422. Vector diagram of vacuum tube compensation 2423. Plate current - plate voltage characteristic of audion 27
List of Curves
curve pageI Variation of "time-constant ratio" to frequency 33
II Animal operating loss due to interference, againstresistance of primary line wire 34
III Chart for the selection of the proper size of primaryline wire for the minimum total annual charge 35
IV Relation of "mutual voltage", "residual voltage" andratio of turns of neutralizing transformer to"impedanceratio" 36
- 1 -
THEORY OF THE TRANSFORMER FOR THE 1JEUTRALIZI1TG OF
POWER INDUCTION IB TELEGRAPH CIRCUITS
I
INTRODUCTION
1. Power Line induction
When two conductors forming a single phase alternating current
line are connected to a source of high alternating potential, this
line has the property of being capable of producing a disturbance
in an adjacent neighboring closed circuit, when this closed circuit
is HOT placed symetrically with respect to the power circuit as in
o o± T
Fig. 1 Section Viewof a Power Line and O Oa Communication Line C &
For instance, consider AB to be a single phase line at a high poten-
tial, and CD to be a telephone or telegraph line. The line AB causes
two kinds of interference in the line CD, namely electrostatic and,
when there is a load on the line or '.vhen the line is long enuf to
have considerable capacity, there will also be electromagnetic induc-
tion
1
W
- 2 -
The conductor A produces an effect in both C and D, as does also
conductor B, v /
\ A m /
C" a J> 2 L—Fig, 2 Longitudinal View of jX'
of a Power Line and a Com- ^ ^munication Line with Trans- > v
position / B \
If the distance at which the line CD follows parallel to AB is con-
sidered as being "2n rT
, and the wires CD be transposed at the dis-
tance V, (see Fig. 2) it may be seen that both G and D affected
by the same influences, precisely, and the resulting disturbances
will be zero. If, as in the case of usual telegraph systems, there
be but one metallic conductor G, the other conductor necessary for
forming the closed circuit being the earth, it will be impossible
to transpose the lines as in the case of two metallic wires. In
this case, (see Fig, 3) the voltage induced must be eliminated by
some other means than geometrclpl transposition. One of the most
frequently and easily applied means is by the use of the Heutraliz-
Transformer.A Bo o
Fig. 3 Section View of -£ r^ tFPower Line and a Com-munication Line of theSingle -oonductor-ground-return type a
Co
Earth
2. The neutralizing Transformer Defined
The purpose of the neutralizing or compensating transformer is
to secure a voltage equal in magnitude, but opposite in phase to
- 3 -
some electromotive force which it is desired to nullify. For exam-
ple, everyone is familiar with the sight of telegraph lines which
parallel railways some of which are electrified from an alternating
current source. There are many places where telegraph lines tra-
verse territory where, for a region of from two to forty miles, these
lines will be paralleled "by alternating current circuits as railv/ays.
in the case cited above, or transmission lines, as in Fig. 4.
<-' Exposure — Singh phase line — "x "miles - - ^/
Station t J~ fe'egraph lines
Apparatus
Fig. 4 Sketch Showing Telegraph Lines Being Paralleledby and Alternating Current Power Circuit.
3. Applications of the Neutralizing Transformer
The proximity of this alternating current power for a long ex-
posure, induces voltage in the telegraph lines, which interferes
with the sending of messages. The only way for this voltage to be
made nil is by the application of its exact opposite. Transposition
of the telegraph wires would serve no purpose, because these cir-
cuits are of the one-wire -ground- return type. With these existing
conditions, it is here that the sphere of this special type of trans-
former comes into prominence. The usual arrangement is to have a
"primary line wire" Dj (see Fig. 5) parallel the exposure. This wire
is in series with the primary of the compensator and is also grounded
at each end, thus forming the return circuit. The secondary coils,
\- 4 -
A-C Paver Line /
Primary Line WireJQOO* Primary
enser
L
Pig. 5 Compensating Device Applied to Telegraph Circuits
equal in number to the lines which are to be compensated, are each
in series with their respective circuits, as shown in the figure.
The condenser in mulitple with the primary is selected with a view
to making the voltage across the primary in phase with the voltage
drop in the primary line wire and in the telegraph lines.
4. Acknowledgements
The writer wishes to acknowledge the invaluable aid given by
Mr. J. V/. Milnor of the Western Union Telegraph Company, Hew York,
under whom (with reference to another project; the initial stages
of this work were done. The writer is indebted to Profesor B. B.
Paine, Head of the Electrical Engineering Department of the Univer-
sity of Illinois who has had the general cupervision and guidance
of this .vork under his care, and to the other members of the Depart-
ment for many valuable suggestions. Particular mention is due in
this respect to Profesor Morgan Brooks who has helped in making the
subject matter clearer and to Mr. W« D. Cannon who has read the
proof of the manuscript.
- 5 -
5. Statement of the General Problem
It is found, in general, that Neutralizing Transformers do not
completely neutralize or compensate; hence there remains a resultant
voltage in the telegraph line, which, if it he of any considerable
value, will cause an economic loss to the company operating the tel-
egraph system, for it is obvious that signal- cannot be transmitted
as fast when there is interference, as larhen there is not. This in-
terference or inductive disturbance is of two kinds:
(a) Interfercnee due to "residual" or uncompensated voltage, which
is due to frequency variation of the disturbing power line from its
normal operating frequency (that is, the "critical frequency" for
which the resonant circuit of the compensator is adjusted), ".Then
this frequency is not that for which the primary of the Neutralizing
Transformer and the shunt condenser was set to secure compensation,
the secondary voltage will fail to completely compensate both by
lack of being the proper phase and correct magnitude.
Fig. 6 Compensation at s'
Critical Frequency
Fig. 7 "Residual Voltageat some Other Frequency
(b) Interference due to induction between secondary coils, of which
there is one for each telegraph line, producing what we have called
a "mutual voltage". This induction is due to the telegraph currents
themselves, flowing thru inductively coupled circuits. The combined
effect of these several lines is felt in each of them. The grouping
of them is shown schematically "by figure 8.I .
A./ unavia
2
JifiMtmBi
Fig. 8 Grouped Secondaries * — "Y^fft
Producing "Mutual" Inter- ^ uwvwl.ferenee
The practical question, then, is: "How may the sum of the inter-
ferences be made as small as possible". This will be answered by
an investigation into the general theory of operation of the com-
pensator. Various circuits will be discussed and the relative ad-
vantages and disadvantages of each type will be pointed out.
II
THE GENERAL THEORY
1. Operation at Critical Frequency
( a) Compensation of Power Line Induction
For this part of tne problem, the chief interest is m securing
voltage of the proper magnitued and of the right phase. With this
in mine, the following considerations are offered.
Assume
:
»• Secondary e m f, equal and opposite to the total in-
duced voltage from the power line for the exposureDD (see Pig. 5).
Primary impressed e m f (see Fig. 9 for vector relation7? -i rr 1 f) "Pat* txt t t»*! ncr i o o»t* e m n ~r\ n» "I"! "Pat* rl d t o i 1 ox*^ 1U1 W XX JLIlg U. J-ct^J- dXJi ctllU. i1 igt JL.L 1UI U.t3vcl-LJLfc?U-
view of the neutralizer primary and shunt condenser.
R, "Equivalent" (copper and iron) resistance of primaryof transformer.
L, Primary inductance.
2p Primary impedance.
C Capacity in parallel with primary.
Impedance of primary of transformer and condenser inmultiple.
*c Resistance of "primary line "ire".
Iz Primary current
Condenser current
I, Total current
p Ratio of primary to secondary turns
9 Phase displacement between primary and line currents.
—E L Voltageu 2irf
tor
- 8 -
across "primaryZ>* ( irequency)
line wire"j
T Time-constant L /R
Then, when neutralisation takes place , e have, using the above no-
menclature and the diagram given below:
1 vectorially and algebraicallysince all are in phase
2r- —r
j
p /—pip
3 EL= RJL
4
5
6
7
r i lip I
f = t>*ur
2P /p s Zp/p-hR.L
from 3 and 4
from 2, and since
sec vector diagram
8 from 6 and 7 and I being commonand mulitplying by cos 9
9/ „ ~7 , Q , „, J. on transforming
10 which, on transposing the term
11"7 _ Hi P CCi^
p(/-/!>
thus giving primary impedance interms of primary line wire re-sisxance, raoio oi xurns , ana.
phase angle (hence, time-con-stant) without regard to thevoltage and currents involved.
Fig. 9 Vector Diagram i
Showing Compensationof Power Line Induction
l<-Za. "= }?~Zp v LRx. .
- 9 -
Having obtained an expression
thing is to find the proper value
relation. Proceeding as follows:
12 T = L?
15 Tuj= Ljl^ - Kf - fan dHp RP
14. <j>~ tan V
15 \ - Zp sin<f>
16 L po^ ^XP = Zp sin<f>
17 ~j/c Xc =j/rZp
18 /c * - lp sm<f>
19 .'./, *»4-XQ=/p Zp
20 mj-X^Zp21 X = —
c Coo
22 s '» £ _ 7
Zoo
Fig. 10 CircuitDiagram forCompensation
for the primary impedance, the next
of condenser to give the right phas
time-constant
fundamental relations (see Fig.12)
from 15
fundamental relations, as also
from vector diagram of neutral-izing transformer, also
from 17 and 18
by eliminating I ; hut
a fundamental relation
from 20 and 21
which is the theoretically cor-rect value of capacity whichwill correct the phase.
-artin tAJJUUJUtMMJUU
- 10 -
Fig. 11 Circuit Diagramof Transformer Primaryand Condenser
" P
Fig. 12 FundamentalVector Diagram
The significance of the above equations is as follows: Regard-
less of excitation current, the value of primary impedance is abso-
lutely determined when the "primary line wire" resistance, ratio of
turns and time-constant of the neutralizing transformer are known.
It is customary in design to select some standard ratio of turns
of primary to secondary, and some time-constant Data will he given
later for indicating the most advantagous method of procedure in the
selection of the proper values. Therefore, knowing the length of
exposure to the alternating current power line, . ith the size of the
compensating "primary line wire" to be used, we thereby predicate
the primary impedance which will give correct compensation.
Having this value of impedance as a numerical quantity, we may
calculate how much of this is resistance (copper ?nd apparent iron
resistance) and how much is reactance, with a vie to altering the
tirne-eonstant , whould the values seem disproportionate. The question
of efficiency in the matter of Neutralizing Transformer losses is
not paramount, since we are merely looking for compensation, and
compensation not only for critical frequency at a predetermined in-
induced voltage, but correction for deviations in the periodicity and
- 11 -
in the magnitude of that induced voltage. This is a radical depart-
ure from the usual type of transformer in which the impressed voltage
is constant to within a few percent. In the case "being dealt with
here, the interference may vary from a small value at no load when
atmospheric conditions are damp, to over 150 volts when the line cur-
rent and conditions for electrostatic induction are most pronounced.
When this value of r has "been selected, and co has been fixed
by the frequency of the line causing the disturbance which is to be
compensated, the angle ? may be found from equation 14, R and L
follow directly from equations 15 and 16. These formulas were of
prime importance as a groundwork for subsequent investigations.
The foregoing quantities give us all the necessary data for
calculating the correct capacity in equation 22. The functions be-
low may be used to state our problem generally, thus
22 Z p- t ( h R,
}Y)
24 W
85 Lp= *; ( Z„ W
26 Cp- o- (Z Pl f)
(b) Mutual Interference between Telegraph "'.'ires
As has been stated before, the compensating voltage is applied
to the telegraph line by virtue of the secondary coils of the neu-
tralizes These coils carry telegraph currents which are pulsating
and in effect like alternating currents of a fluctuating number of
cycles per second. 1 hile the relation at any moment of one signal
current to any other is a random one, on the average, the effect of
the interference from a number of circuits may be taken as a propor-
tion of the interference which would take place with a lesser number
- 12 -
of lines, "but all operating in unison. In practice, the average
effect of 40 circuits operating is about the combined effect of 10;
of 20, as 8; of 10, as 7; and of 6, as 5. We are furthermore assum-
ing that the key frequency of the telegraph signals, is, on the whole
that of the disturbing power line or railway. Mathematically, this
quantity of disturbance may be obtained from the considerations given
below (see Fig. 10). Any given secondary conductor has signal cur-
rent flowing in it, and we may take this as approximately one -tenth
ampere. The e m f which this particular secondary w ill induce in
each of the others will be the product of the current of that secon-
dary by the "equivalent impedance" of it. The equivalent impedance
depends upon the ability to load the resulting primary circuit and
the other secondaries, as the diagram (see Fig. 10) will show. For
purposes of computation, the primary may be considered as being com-
posed of three circuits in parallel: 1. Primary of transformer, 2.
Condenser, 3. "Primary line wire". This latter branch is completed
by the ground return. The secondary loadings will be the various cir
cuits completed by their respective ground returns. The equivalent
plan is shown by Fig. 13
o,Ltj>*jL*L,vu** secondary
r<
Fig. 13 Diagram ofEquivalent SecondaryImpedance of System
flu
"
Owing to the fact that each telegraph circuit has a very high
resistance which lies in the neighborhood of several thousand ohms,
such that even the parallel arrangement of a considerable number
would have a resistance which would be much greater than that of the
primary line wire, we shall neglect the conductivity of these paths.
- IS -
We are left, the, with the three parallel primary circuits, the dia-
gra, being shown "by Fig. 14tiLAt-tjat tOott>nt>toao«(ni_
Fig. 14 Circuit ofApproximate Equiv-alent SecondaryImpedance
C
^AAAA/VVVVVV
The following additional nomenclature is introduced at this
point, the rest being used in the same sense as section (a).
As surne :
T,
JL.
I.
El
Admittance of primary of neutralising transformer
Susceptance of condenser
Conductance of "Primary line wire"
Total admittance of all three branches in parallel interms of secondary admittance
Total "Equivalent secondary impedance"
Signal current in telegraph line
Yoltage induced in each secondary coil, due to impedancedrop in secondary coil under discussion
Then
:
27
28
29
30
Zp ^ Rp+jX = Zp ( cos f +j s'wf)
c-s//?
£.
L " p cos f
31
32
see Fig. 12
and
from 23
from 11. Having our separateelements, we may now considerour admittances, thus
or, from 27, 29 and 30
Y - p1
]^—,—'. + ; cu ,
f-p) J
33 5-~ZF (cos
<f>-tj sin
<f>
)
+
factoring
jCtP
34
- 14 -
~ £~ \ l + Ism* + P&st 1~Zp L cos f + j sin
<f>i-preducing to common denominator
35 —Z
f' ~P
~*~J sm^ c °s<t> ~ slii
Z
t -Jpsin<t> cosj> +psj»z<j> +pco/j> f-jp si/i4 cos
<f>1
z/» 6~p)( cos d> +j si*?*) J6~p)( cosj> tj S/#<j>
)
collecting terms
36 Y. -- ^ \ '~P V s 'n t cos f~ sw ¥ ml simplifying
37 \~- \' +
l^ C05 t- s '»
z
t] trigonometric suds ti tut ion
38 Y. = -£\ coszj>i-js,nt cosf 1 factoring
~Zp L (i-p)( t°&4 f j Slyur)
39 Y,* 4Z[ «**( ce'ttjs>»t) l cancelling^ 7p L (i -P) ( cost +) smf)
-1
40 Yj = 4ZJfit from 11
41 X s PzrS; inverting
p
This important formula tells us all there is to be known with
reference to "equivalent secondary impedance" when the signal cur-
rents average the critical frequency (equation 42). Owing to the
fact that this is a step-up transformer, "p" cannot possibly equal
unity unless H is equal to zero, or Z equal to infinity, or unless
the time-constant is infinite (see equation 11). Furthermore, it
has been found from experience, that the best values of "p" are in
the neighborhood of .9, because any excess of this makes a big in-
crease in the cost of the transformer on account of the high time-
constant required and is not warranted in the increased advantages
of lower mutual impedance. Briefly, then, this equivalent impedance
does not depend upon the constants of t"he transformer, except as
regards the ratio of turns; but does defend upon the resistance of
- 15 -
of the primary line wire. It is therefore important to have the pri-
mary line wire low in resistance. The relationship of the proper
size primary line wire will "be more fully discussed in a following
section (see chapter IV, section 2 A),
Having determined this equivalent impedance, the voltage caused
by one circuit in each of the others is:
43 E-'s '"Zj^l'u ot finally, from 42 an- 45
The total effect of "n" circuits may bo then ascertained from data
given on page 12 near the top of the page.
These results are approximate, because we have assumed telegraph
conductors of such high resistance as to have an inappreciable effect
on the equivalent impedance of any secondary. Also this is approx-
imate in the matter of the combining effect of several circuits, the
telegraph signal current and the key frequency. The latter is not a
fixed number, but depends upon the reat of transmitting and the char-
acters being used.
"'hen there is no variation in the magnitude of the induced vol-
tage, but the frequency changes from the critical value for which
the condenser was selected, there will be a "residual" or uncompen-
sated voltage, (compare Pigs. 6 and 7) which may be predetermined
for any frequency, primary line wire resistance, ratio of turns and
time-constant, which will be treated in the discussion following.
In addition to the nomenclature used above, the following new
volts per circuit.
2. Operation at Hon Critical Frequency
(a) Residual Voltage
- 16 -
terms will he introduced:
"Residual" or uncompensated voltage
ru frequency / 10
a© "ax 10 13 "
45 Er^^t'Es see Figs. 6 and 7
46 Ey= E
p+ E
L
47 Er ^Z^/L drop thru primary; now Z , theimpedance of the parallel "branchis found as follows
48 Z = Rp + L- p (*> fundamental relations
49 Y ='
51 y s I Cou seperate admittances, havingc J for a combined result
52 -—f ^ y"co 2nd-, on invertingR p i-jLuj
J
55 Z«_( simplifying
~o—?—;— + / C
54 Z^ = - ^ e +j L-
i -h Cuu Rp - Cuj Lp
55 » A7^ 4* 60 eliminating complex denominator
0-L,u>C) + j Coo Rp56 Z^- (R p + J Lru>)(i- L p Cqj - j RpClo) collecting component terms
57 Z - & +\\ Lu>-RlCu> -Cl\u> 3l
58 Z = t^Lig 27TQ^ - CRliirQ^ z£L^MJ^hdl
which is the form for rapid com-putation ..ork
Thus, from 3 Lp
, C and V we find the VECTORIAL expression for
the impedance of the parallel circuit of the transformer primary
- 17 -
and the condenser. .We then add this quantity VECTORTALLY to R which
gives us the vectorial value of the total series impedance, Z .
Prom Z,assuming the magnitude of the total interfering voltage to
he 100, we may find I . Knowing I and the impedance of each sec-
tion of the series parts, we may find the vector value of the voltage
across the primary. This may be seen from the equation given below,
59 100 = Zr 4 = £ Zc + HJ/L and
60 F - V l knowing the ratio of turns, wep
-
Lhave E
61 ELS - §LP := (j- which enables us to find E as
p ~~p~ a percentage of 100 from equa-tion 45
v'/e have made extensive use of equations 49 and following in the
determination of data for the relation of the residual voltage to
primary impedances for various time-constants (see Curve IV at the
end of this work).
(b) Mutual Interference
When the signals are not being transmitted with the same frequeue
as the critical one to which the resonant circuit is set, the expres-
sion for the "Mutual Interfering Voltage" becomes more complex. In-
stead of having the equivalent circuit composed of the transformer
primary and shunt condenser of extreemly high impedance, this quan-
tity is much lowered, particularly if the resonance be sharp. The
reader is again referred to Pig. 14 with the mention that the sol-
ution is similar to that given for critical frequency, except that
no value is taken for that frequency, that is, this case is general.
As in the preceding, the total admittance is the sum of the separate
admittances , thus:
- 18 -
62 X -P* [ r IjL u>+^u< which is the general form of 31;
' r and reducing this to common de-nominator
and we may find the total im-pedance
collecting the "j" terms
65 7 - 1 ^ (Rr +jL? UJ )
P2
(Ru +Rp-RL CLP^ L
) -hj ( Ctu RcRr + LpU;)
clearing complex terms fromdenominator
66 Z - 1 R^(Rr+>L Pu>XR^RP -RL.CLr^-j{RP ^C<"+Lr<~))* r (R^Rp-RlCLpCo*) 2
+( C^R.RP +L,<*>)Z
expanding
67 2^= -L *l[ ft.^+Rp^RuRpCLp^-jR.RpCLo -j RP L P u, +jR,LF «>-jlia\JtRpHCLP ujt+ lA^j
P2 (R^Rp-FtuCLp^) 2- + (R^RF Coo +Lpu>) z
cancelling like terms
68 ^Rt- tWr+ftp -RcRPCLP uJz i-RL RpCLpUJ
J
-i-L^L-hj {-RlR^C^L^R^Lp^r.l^ -R^CL^u, 3
)]pZ
(R.+Rp -RuCLp^r + (R, R.C^ + L P<~)
C
rearranging
69 7^Bf I R. & t*p +L P^ +j { R.LpUJ-
R
L RR2
Cu> -R^Ct}* u>3}]
pZ(R.-hRp-R^CL F cu 2
)i+ (Rp Rt CuJi.Lp^) z
and, in form for computing,similar to equation 58 in type
P [Rp+ /?t -^1^7^^Having this equivalent secondary impedance, the mutual voltage
is found as in the case for critical frequency, see page 14. This
formula, like those from 58 to 61 inclusive, see page 17, was the
basis for a set of curves (see Curve IV).
- 19 -
III
SPECIAL TYPES OF UEUTRALIZER
IBIRODUG^OEY. Among the special types of compensating devices
which oecured to the writer, two will be mentioned, and a brief out-
line of the theory of each will be given. After the investigation
was fairly started and the negative results of these forms forseen,
the study was prosecuted vigorously with a view to proving mathemat-
ically the fact that the simple type would of ~er a minimum impedance
hence a less interfering mutual voltage to the telegraph circuits.
1. Parallel Compensators
In the effort to distribute the impedance by means of parallel
branches, and in that way cause the total amount of the same to be
the least, the following device was tried. Instead of having one
core having all the secondary coils wound thereon, it was decided
to study the effect of having as many small transformers as there
were lines, the aim being to eliminate the inductive coupling between
circuits. The total failure of such a scheme will be apparent.
(a) Compensation of Power Line Induction
This argument is very similar to that given on page 7ff , which
see. Assume
R5 Resistance in series with each compensator
n Humber of circuits
R "(R- nR )
- 20 -
The arrangement of these parallel circuits is shown "by Fig. 15
Fig. 15 SketchShowing ParallelCompensators
It will also be noted that there must he as many individual conden-
sers as there are neutralizing transformers. The manner in which
this arrangement works out, when adjusted correctly and when the
power line induction frequency is the "critical" frequency, may he
Referring to the nomenclature which has been used previously
in addition to that given above (page 19):
seen from Fig. 1G
Fig. 16 Vector Diagramfor Compensation withParallel Arrangement
71P n
theory similar to that given inequations 1 to 11 inclusive
72 from 71; eliminating I
75 multiplying by "nn n
74P
factoring
75 an expression for the impedanceof each branch, but
76 *•~~ —7
1
0-p)
r
coscf>
(i-p)
- 21 -
Fig. 16 and equation 71
from 7G and 77
This gives, it may ".be seen, a larger value for the individual in-
pedances. Furthermore, in order to determine this quantity, it is
necessary to assume two more factors, namely "n" (the number of cir-
cuits) and "R " (the resistance in series with each transformer.
(b) "Mutual Interfering Voltage"
The effect of this e m f is discussed below. It will be seen
that metallic connection of the primaries plays a more detrimental
role than simply magnetic coupling between the secondaries, when
these are wound on the same core. The equivalent secondary impedance
of any coil may be considered from its loading as in Fig. 17
UJULOJt l_g I o noet _ _
Fig. 17 Equivalent Sec-ondary Impedance withParallel Compensators
—\p-
II-
The argument is built from Fig. 14. At critical frequency, the pot-
ential drop across Z (that is, Z in parallel with C) is in phase
with the vector sum of the currents of those two branches; therefore
Z , taken as an entity, functions as pure resistance. Our diagram
then becomes as in Fig. 18. When primaries are in parallel, the ef-
ect of the "nth" secondary on the other ( n - 1 ) , is found as fol-
lows. The other nomenclature used than that given below, is similar
to that of the preceding sections:
R" Resistance of ( n - 1 ) circuits in parallel
R" 1 R" in parallel with R
- 22 -
jULaejULtLaitL.
Fig. 18 Effective Re-sistance of CircuitsOperating at CriticalFrequency
AWWV-
-AMAA.
Fig. 19 Reduced Equi-valent Diagram in termsof Secondary Values
79 R *= 2^ ± # T
(1-1)
80 /?"'= -£J$L.
the resistance of ( n - 1 ) cir-cuits in parallel; and thisquantitjr in parallel with R
and this quantity in series withB
which gives an equivalent sec-ondary value
81 /?""= /TV IT,
82 J .
This plan will not reduce the mutual interference, because, altho
increasing R lessens the amount of disturbing current in the primary
it at the same time increases the equivalent secondary impedance; con
sequent ly the potential drop across that impedance. This is because
of the fact that the signal currents are adjusted to nearly constant
value, regardless of the impedance to be overcome. Another point
must be considered in the operation of this device (and which holds
true for any compensator working on the resonance principle) is that
the telegraph signals are sent with a varying rapidity; thus a vary-
ing equivalent secondary impedance is offered those signal currents
because the impedance of a resonant circuit depends u^oon the frequen-
cy. This may offer a serious objection when the equivalent secondary
impedance is relatively large and the resonance sharp, in that it wii!
damp out signals of resonant frequency.
As an illustration, consider the inteference from a system of
this type in the special case of R R , then
now when Z is considered, itmay be shown that its value islirge compared with R
is approximate; also the value( n - 1 ) is not from ( n )
and this quantity in parallelwith R
another working assumption whichmay be justified by experienceis, when the number of lines islarge Z /n = R
and this in series with R = R
which, in terms of secondary val-ues, gives
There is nothing mysterious in these assumptions, for the amount of
error made by their use, is insignificant, also we may make Z almost
any value we choose to come within the range of the case Z /n = R
In the simple circuit, see equation 42, we find the conditions
much better than with the case taken above, thereby proving the ad-
visability of abondoning the scheme just preceding. With the theo-
retical limit of workability, there would be 1.5 times the interfer-
ence with this kind of neutralization as with the single core compen-
sator.
85 ^=4^
84 /?"=(n-i)
85 /?"=
n
86 R"~ J*%R"+RL
87 /?"'» 5* = £
88 z; =/?""« R, +RL
89 Z a tOt
- 24 -
2. Compensation by Audion Bulbs
\ Power L'tne Expire /
Fig. 20 CircuitShowing Compen-sation by Audions
Fig. 21 Plate Current -
Grid Voltage Character-istic of Audion
^.....Gnri TransformerISJJUL
Paten-
sums-
ft'omete/m
MMSLchokeCoi]
' Transformer
^jlt m-~f>}
[Y ntx
-UUM
t5ujulsl. J
jam.
s
OAMr
line # I
J£2
GT '6T T
Fig. 22 Vector Diagramof Compensation
- 25 -
(a) Theory Applied to Correction of Interference
In this connection, it is necessary to examing what the factors
for compensating at frequencies other than the critical one, are,
and conditions modifying mutual voltage. The diagram given (see Fig.
20, shows three telegraph lines connected to the apparatus which
operates as follows:
The compensating line being grounded at each end, is in series
with the primary of a transformer. This is the grid potential trans-
former. The primary of this is in series with a condenser to secure
the proper phase relation, (see Fig. 22 for vector relationships).
The secondary potential secured by moans of this transformer gives
the same voltage to each filament - grid circuit of the several tubes
Since the filament - grid circuit is practically open ( as regards
the internal impedance of the tubes ) the telegraoh currents cannot
"back-fire" into it and produce mutual interference, as was the case
with all devices explained hitherto.
The same plate battery serves for all the tubes, the alternating
current being excluded from these separate circuits by means of choke
coils which of ror at tho sane time, on accoimt of their low copper
resi3tancos, very little obstacle to direct currents. In the same
manner, the direct current is insulated from the compensating circuit
b#- means of a condenser in series with that circuit asd set for re-
sonance with the transformer at critical frequency. A potentiometer
in each grid lead regulates the grid potential in such a manner that
modulation takes place on the straight line oortion of the "grid vol-
tage - plate current characteristic (see Fig. 21). This being so,
the plate current will flow thru the primary of the transformer cir-
cuit in quadrature with, and proportional to, the disturbing voltage.
- 26 -
See Fig. 22. Since the condenser and primary of the grid transformer
act much like an effective resistance if near the critical frequency
,especially when the time-constant of that transformer is poor, we
will have a current flowing thru that circuit (the primary line wire-
primary condenser - primary of grid potential transformer ) , which
will be in phase with the e m f induced from the power line into the
parallel exposed telegraph lines. The flux and current vectors (see
Fig. 22) will he nearly coincident and the secondary voltage will he
at a quadrature relation with the grid potential transformer flux,
that is, roughly 90° from the power induction. But when we are work-
ing on the straight portion of the audion characteristic (see Pig. 21)
pir tune current o;; ne of the same phase as the grid voltage. This
tube current is the one which operates the neutralizing transformer
and is substantially in phase with the flux of that transformer, for
the transformer is not delivering power and therefore does not need
to furnish a component of primary current to take care of any second-
ary current, therefore the induced voltage to the secondary of the
compensating transformer will lag behind the plate current by 90°, or
the voltage induced by the power line by 180°.
If the time -constant of the neutralizing transformer by small,
but more so on account of the high internal impedance of the tube,
the resonance curve will be broad, and compensation will take place
under quite a deviation from the critical frequency. This may be
seen by considering a circuit of resistance, inductance and capacity
in series (as the plate circuit, primary of transformer and condenser)
This arrangement is shown by Pig. 20
(b) Results
It will "be found in the use of tubes, however, that the economy
is low, for the following reasons: (a) the plate current is small
with a small bank of tubes, hence the ratio of turns of the neutral-
ising transformer will have to be high in order to neutralize the
secondary voltage. This . ould be satisfactory if this was the only
thing which had to be done, but it is not, for telegraph currents
must be practically unimpaired by this appended circuit. How, with
the large number of turns in the secondary which would be necessary,
there would be heavy impedance to the secondary currents. This
would be serious, but not fatal, for the impedance is nearly constant
as regards the amount of current being transmitted. The difficulty
which remains to be overcome is the electromotive force which would
be induced into the primary of this compensator and thus function in
conjunction with the plate battery. Altho the characteristic of
this plate current - plate voltage curve is nearly horizontal, to the
right of A (see Fig, 25), a difference of voltage of the order of
one hundred or over, would take the plate current below that steady
range, and thus affect the entire working an transformation ratios
of the tube. The system must be one in which the neutralization does
not interfere with the signal currents and vice versa. This may be
done, as pointed out before, by a sufficiently large number of tubes
to render the total impedance low; but from the tubes now available
on the market, this would be economically out of the question.
!Fig. 23 Plate Current ^
Plate Voltage Charac- *teristic S;
Plate Voltage
I
- 28 -
COIICLUSIOIJS
1. General Observations
The operation and theory of the neutralizing transformer have
been discussed from whieh the following facts have, been noted:
A. The time-constant should be small to -insure broadness
of resonance for taking care of slight deviations from the critical
frequency. This time-constant will vary somewhat on account of the
variation of the impressed frequency, ^he explanation for this is as
follows: The definition for the time-constant is lp/H F ,
Now, in our
transformer, R is the effective value, and, as such has not only the
copper component of resistance, but the "equivalent iron resistance"
of hysterisis and eddy losses. These vary approximately with the
square of the frequency, so that, when the range of period of the
e m f which we have dealt with is large, there is an apparent change
in the value ofY*. This may be seen graphically from Curve I at the
end of this thesis.
B. The compensator should have a characteristic such that
it can readily accomodate itself to the wide range in impressed volt-
ages to which is will be subjected. This is a snocial study in that
connection.
C. In the case of mutual interference at critical frequen-
cy, the only way to reduce it is by having the ratio of turns as near
the maximum as economy will permit, and at the same time reducing the
resistance of the primary line wire as much also as the economy will
warrant (see Equation 11).
D. The method of parallel circuits, at "best, does not
give as good results as the simple general case first treated, for an
improvement on one factor is accompanied by an overbalancing detrimenl
in some other or others.
E. it is found in the case of vacuum tubes, that the cost
of the tunes, the maintaining charges and other items do not offset
the expense of a large size primary line wire. The chief obstacle is
the high internal impedance of the bulbs and their very small output
capacity.
2. Some Applications of the Theory
We shall set forth briefly below, some of the practical results
of this study on the Neutralizing of Power Induction.
A. Mention has been made of the "primary line wire", and
of the desirability of having its resistance lew (see equation 11).
It was stated in section 1 (b) of chapter II, that current set up by
"mutual interfering voltage'' caused an economic loss to the interests
operating the lines. This has been figured out in terms of interfer-
ing current. With this as a basis, the writer proceeded to balance
this charge due to interference against that of the primary line wire,
since it has been seen that a heavier primary line wire, by virtue of
its lower resistance, will cause less interference than a smaller one
would do
.
It is reasonably safe to assume a resistance of about 2000 ohms
for the average iron telegraph with which ve are dealing; also a /alue
- so -
of l/lO ampere for the message current. . e have already shorn thatj
the mutual voltage is proportional to the equivalent secondary imped-
ance and this is directly proportional to the resistance of the pri-
mary line wire (equation 11). Hence, e have a direct relation be-
tween the resistance of the primary line wire and the annual charges
due to interference. We may establish another relation "between the
resistance of the wire to its length for a number of sizes and the
same relation between annual charges to given length for the various
sizes used. This will furnish a chart from whieh the proper size
wire may be selected to give the minimum total annual charge for any
given length of exposure (see chart - curve III).
Illustrative Example on the Use of Chart: Assume we have a twenty
line system and that there is an exposure to alternating current
power for a distance of twenty five miles. First, follow the hori-
zontal line for "25 miles" on the chart, until intersects trie line
for 400000 circular mils both the right and the left, which, ih the
former case is the nearest line, while in the latter is the farthest
one. At the point of intersection ih each, respectively, follow the
vertical to the horizontal axis on the left and determine the "An-
nual Charges for Line", which, it may be seen for 20 wires for 25
mile exposure, is $3700, The vertical on the right is followed until
it intercepts the curve for "20 wires" (found in the first quadrant),
from which point a horizontal course is taken until the "Annual Char-
ges for Interference" axis is intersected, which, in this case, is
at $800. Our total annual charges, then, using 400000 circular mils,
is $4500. By trying other sizes, it will be found that #000 B. & S.
gives the minimum total annual charge which is 23500, One also sees,
pwing to the fact that the lines in the two lower quadrants are
straight lines and that those in the first have little curvature,
- 31 -
that nearly a constant size wire will give the most desirable results
for ANY length exposure, it "being merely, a problem to fine out the
size which takes care of any given number of telegraph lines best.
A separate view of the "Interference Charges',1 to that of the "Resis-
tance of the Primary Line Wire" is shown in Curve II at the end of
this paper.
B. In the case of automatic sending apparatus, the fre-7
quency of the signals may, on the average, be assumed as 50 cycles.
When we are compensating a power line, the normal frequency of which
is 60 cycles, advantage may be taken of the difference of the tele-
graph operating frequency from the critical one, in the matter of
resonance. What is desired is a broad resonance curve over the range
in which the power frequency ordinarily varies, and a sharp curve
for other frequencies, particularly 50 cycles. This sharp curve
means a lo.v equivalent secondary impedance, hence a low drop due to
the telegraph currents, hence a low mutual voltage in the other sec-
ondaries of the transformer.
Certain relationships which alter the character of this reson-
ance curve may be studied in the light of formulas 58 and 70. From
these equations, we have the basis for plotting curves which will show
us the most advantageous ratio of turns, time-constant, etc., for a
given resistance of the primary line wire. A family of curves for
residual voltage, mutual interfering voltage and one for the ratio of
turns may be seen from Curve sheet IV. The more important character-
istics of these curves will be pointed out. The most convenient
abscissa to ahich to plot these curves Y/as found to be the product
of the primary impedance at critical frequency by the time-constant.
Both kinds of interference are shown, with the ratio of turns for
each, so it is simply a problem of selecting that sum which gives
- 5-2- 1
the minimum total interference. Having decided on the, value of Z,
and p, we are ready for our design.
From the curves, it may be seen that:
1. E R is nearly proportional to the frequency deviation,therefore, a 1/2 cycle variation either way from normalgives E
R half of the original value.
2. E^is less with small time-constants.
5. £ R is less with high values of p.
4. Br is HOT changed by when Zpis altered in the same pro-
portion (see equation 58).
5. Eflis a function of the number of circuits exposed andto the transmitting current.
6. Em is less with large time-constants
7. E^is less with low values of p
8. Enis DIRECTLY PEOPORTIOHAL to R Pwhen "pis .altered in thesame proportion (see equation 70).
For carrying the work forward, the next step would involve trying
out some spefic design. The laboratory model would be tested under
conditions resembling, in so far as possible, those which the appar-
atus would be expected to remedy, and, if found satisfactory, would
be installed in an operating line.
